Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates

Abstract

Based on detailed three-dimensional (3D) finite element analyses, elastic fields in front of blunt V-notches in finite thickness plates subjected to uniaxial far-end tensile stress have been investigated. By comparison with the corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) Kt, which is higher in finite thickness plates than in the plane stress and plane strain cases. When the notch angle is smaller than 90°, the SCF is insensitive to the notch angle, but has close relation with the dimensionless plate thickness. With the notch angle increasing further, the SCF decreases and the effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress σyy normalized by its value σyy0 at the notch-root with the distance x from the root normalized by the root-radius ρ, is insensitive to the plate thickness and coincides well with the two-dimensional (2D) planar solution. (3) The 3D distribution of the out-of-plane constraint factor Tz=σzz/(σyy+σxx) is controlled by the plate thickness (B), the notch-radius (ρ) as well as the notch angle (β), but for deeper V-notches with β≤90°, the distribution of Tz coincides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of Tz is presented. (4) The distribution of the in-plane stress ratio Tx=σyy/σxx in front of the 3D V-notch is nearly independent of the plate thickness and coincides well with the corresponding 2D solutions when the opening angle β is smaller than 120°. (5) The gradient of the out-of-plane strain ezz is significant near the free surface in finite thickness plates. On the free surface, the ezz can be 3.5 times the value on the mid-plane, and the through-thickness gradient of the ezz increases with decreasing notch angle. It is of interest to note that most of the field quantities ahead of V-notches are insensitive to the notch angles when the notch angle is smaller than 90°.